Abstract We propose a protocol that allows to assess the precise correspondence between thought and practical experiments, a critical point for addressing experimental clumsiness in a test of macro- or micro-realism. Two-time generalized von Neumann measurements of properties <?CDATA $\mathcal{A}$?> A and <?CDATA $\mathcal{B}$?> B are shown to obey the so-called no-signaling in time condition for initial states defined as an incoherent sum of eigenstates of <?CDATA $\mathcal{A}$?> A . An experiment for witnessing the use of this type of measurements in the laboratory is then devised by proving the existence of five conditions that have to be fulfilled by any generalized von Neumann measurement. Ensuring the use of this type of measurements and then testing the no-signaling in time condition for a range of system-meter coupling strengths allows to test realism in a highly reproducible manner and to critically narrow the so-called clumsiness loophole. The resulting protocol is applicable to general (not only dichotomic) variables, and it is employed to show, both analytically for general systems and numerically for a collection of harmonic oscillators, that quantum systems made of a large number of uncorrelated particles are genuinely macrorealist, i.e., realistic with respect to all intensive properties at any time.
Abstract We propose a protocol that allows to assess the precise correspondence between thought and practical experiments, a critical point for addressing experimental clumsiness in a test of macro- or micro-realism. Two-time generalized von Neumann measurements of properties <?CDATA $\mathcal{A}$?> A and <?CDATA $\mathcal{B}$?> B are shown to obey the so-called no-signaling in time condition for initial states defined as an incoherent sum of eigenstates of <?CDATA $\mathcal{A}$?> A . An experiment for witnessing the use of this type of measurements in the laboratory is then devised by proving the existence of five conditions that have to be fulfilled by any generalized von Neumann measurement. Ensuring the use of this type of measurements and then testing the no-signaling in time condition for a range of system-meter coupling strengths allows to test realism in a highly reproducible manner and to critically narrow the so-called clumsiness loophole. The resulting protocol is applicable to general (not only dichotomic) variables, and it is employed to show, both analytically for general systems and numerically for a collection of harmonic oscillators, that quantum systems made of a large number of uncorrelated particles are genuinely macrorealist, i.e., realistic with respect to all intensive properties at any time.
We propose a test of macrorealism that exploits the contextuality of two-time correlation functions to escape the so-called clumsiness loophole that plagues Leggett-Garg inequalities. The non-contextuality of reduced joint probability distributions is proven to be an unequivocal criterion to guarantee that measurements are carried out in the ideally-weak measurement regime of a class of generalized von Neumann measurements. In this regime, testing the so-called no-signaling in time condition allows to uncontextually ascertain whether a property of a given system is macrorealistic or non-macrorealistic. The resulting protocol allows for tests of macrorealism in situations where Leggett-Garg inequalities and ideal negative measurement cannot be used at all.
Macrorealism, the notion that macroscopic physical properties are well defined at all times and that it is possible to measure the properties without disturbing them, is tricky to test in an experiment, by admitting the ``clumsiness loophole.'' Here, a compatibility condition is found, so that a generalized version of macrorealism can hold for every initial state. This allows one to design stricter experimental tests of macrorealism for which an explanation in terms of ``clumsy'' measurements is harder to justify.
I study several aspects of tests of macrorealism (MR), which for a given data set serves to give a quantitative signal of the presence of a specific notion of non-classical behaviour. The insufficiency of classical understanding underpins both the paradoxes of quantum mechanics, its future technological promise, and so these tests are of interest both foundationally and pragmatically. I derive generalisations of the Leggett-Garg (LG) inequalities and Fine's theorem, which together establish the necessary and sufficient conditions for macrorealism. First, I extend these conditions to tests involving an arbitrary number of measurement times. Secondly, I generalise them beyond the standard dichotomic variable, to systems described by many-valued variables. I also perform a quantum mechanical analysis examining the interplay of different conditions of MR. I then develop the theoretical framework to support tests of macrorealism in continuous variable systems, where I define variables based on coarse-grainings of position. I calculate temporal correlators for general bound systems, and analyse LG violations within the quantum harmonic oscillator (QHO), in its energy eigenstates and coherent states. I analyse the precise physical mechanisms underpinning the violations in terms of probability currents, Bohm trajectories. Staying within continuous variable systems, we outline a different approach to meeting the invasiveness requirement of LG tests. Reasoning that we may approximately non-invasively measure whether a particle crosses the axis, we measure an object which is related to the standard correlators, and derive a set of macrorealistic inequalities for these modified correlators. We demonstrate violations of these modified LG inequalities for several states within the QHO.
This work will incorporate a few related tools for addressing the conceptual difficulties arising from sewing together classical and quantum mechanics: deterministic operators, weak measurements and post-selection. Weak Measurement, based on a very weak von Neumann coupling, is a unique kind of quantum measurement with numerous theoretical and practical applications. In contrast to other measurement techniques, it allows to gather a small amount of information regarding the quantum system, with only a negligible probability of collapsing it. A single weak measurement yields an almost random outcome, but when performed repeatedly over a large ensemble, the averaged outcome becomes increasingly robust and accurate. Importantly, a long sequence of weak measurements can be thought of as a single projective measurement. I claim in this work that classical variables appearing in the macro-world, such as centre of mass, moment of inertia, pressure and average forces, result from a multitude of quantum weak measurements performed in the micro-world. Here again, the quantum outcomes are highly uncertain, but the law of large numbers obliges their convergence to the definite quantities we know from our everyday lives. By augmenting this description with a final boundary condition and employing the notion of "classical robustness under time-reversal" I will draw a quantitative borderline between the classical and quantum regimes. I will conclude by analyzing the role of macroscopic systems in amplifying and recording quantum outcomes.
We consider two different types of conditions which were proposed to test macrorealism in the context of a system described by a single dichotomic variable Q. This is the view that a macroscopic system evolving in time possesses definite properties which can be determined without disturbing the future or past state. The Leggett-Garg (LG) inequalities, the most commonly studied test, are only necessary conditions for macrorealism, but, building on earlier work J. J. Halliwell, Phys. Rev. A 93, 022123 (2016), it is shown that when the four three-time LG inequalities are augmented with a certain set of two-time inequalities also of the LG form, Fine's theorem applies and these augmented conditions are then both necessary and sufficient. A comparison is carried out with a very different set of necessary and sufficient conditions for macrorealism, namely the no-signaling in time (NSIT) conditions proposed by J. Kofler and C. Brukner, Phys. Rev. A 87, 052115 (2013) and L. Clemente and J. Kofler, Phys. Rev. A 91, 062103 (2015), which ensure that all probabilities for Q at one and two times are independent of whether earlier or intermediate measurements are made in a given run, and do not require (but imply) the LG inequalities. We argue that tests based on the LG inequalities have the form of very weak classicality conditions and can be satisfied in the face of moderate interference effects, but those based on NSIT conditions have the form of much stronger coherence witness conditions, satisfied only for zero interference. The two tests differ in their implementation of noninvasive measurability and so are testing different notions of macrorealism: the augmented LG tests are indirect, entailing a combination of the results of different experiments with only compatible quantities measured in each experimental run, in close analogy with Bell tests, and are primarily tests for macrorealism per se; in contrast, the NSIT tests entail sequential measurements of incompatible quantities and are primarily tests for noninvasiveness.